I recently bought canon t3i and started using it. I am interested in learning photography. As a first step, I tried setting the camera in AV mode and set the f number to 3.5 (lowest possible on 18-55 mm kit lens). Even after setting the f value to the lowest possible, I see that the background is still in focus (not blurred at all). Can you please help me?

I am surely missing something. Please let me know how can I get the blurred background?

The amount of defocus varies on several factors. The f number is one of them. Also influencing the apparent degree of blur are the focal length of the lens, and the relative distance between subject and background.

To get f/3.5 I take it you were using the lens at 18mm? Because of the wide angle, the degree of blur looks smaller, so more appears to be in focus. If you go to the 55mm end, even though it is f/5.6, you can get more apparent background blur.

If the subject is closer to the camera and you focus on that, the background becomes more defocused.

Have a play with that and see how you get on. If that still doesn't give enough of the blur effect, then a different lens may be required. For example, the cheap EF 50mm f/1.8 II lens would give significantly more potential in this respect. It does depend on the type of shot you are doing if that would be suitable or not.